Derivative of 3cosx
Derivative |
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d/dx(3 cos(x)) = -3 sin(x) |
Alternate form |
3/2 i e^(i x) – 3/2 i e^(-i x) |
Roots |
x = pi n, n element Z |
Series expansion at x=0 |
-3 x + x^3/2 – x^5/40 + O(x^6) (Taylor series) |
Indefinite integral |
integral -3 sin(x) dx = 3 cos(x) + constant |
Global minima |
min{-3 sin(x)} = -3 at x = 2 pi n + pi/2 for integer n |
Definite integral over a half-period |
integral_0^pi-3 sin(x) dx = -6 |
Definite integral mean square |
integral_0^(2 pi) (9 sin^2(x))/(2 pi) dx = 9/2 = 4.5 |